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Exploration 2. Suppose p is prime and z € Up such that ordp(z) = 7, and let q=z+z² − z³ + 24 – 25 – 26. Show that q² - -7. What if ord p(z) = 11 -11? Or maybe = ? Can you construct an element q from z such that q² q² = 11 ?

Exploration 2. Suppose p is prime and z € Up such that ordp(z) = 7, and let q=z+z² − z³ + 24 – 25 – 26. Show that q² - -7. What if ord p(z) = 11 -11? Or maybe = ? Can you construct an element q from z such that q² q² = 11 ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exploration 2. Suppose p is prime and z € Up such that ord, (z) q=2+2²-2³ + 24 - 25 - 26. Show that q² -7. What if ord p(z) = 11 ? Can you construct an element q from z such that q² = −11 ? Or maybe q² = 11? - = = 7, and let
Transcribed Image Text:Exploration 2. Suppose p is prime and z € Up such that ord, (z) q=2+2²-2³ + 24 - 25 - 26. Show that q² -7. What if ord p(z) = 11 ? Can you construct an element q from z such that q² = −11 ? Or maybe q² = 11? - = = 7, and let
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